Problem: What do the following two equations represent? $5x-y = 3$ $2x+10y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $5x-y = 3$ $-y = -5x+3$ $y = 5x - 3$ Putting the second equation in $y = mx + b$ form gives: $2x+10y = 5$ $10y = -2x+5$ $y = -\dfrac{1}{5}x + \dfrac{1}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.